Fred is an old man. He lived one-eighth of his life as a boy, one-twelfth as a youth, one-half as a man and has psent 28 years in his old age. How old is Fred now?
what is psent?
solve
x/8 + x/12 + x/2 + 28 = x
multiply each term by 48 ....etc
Let's calculate Fred's age step by step.
Step 1: Calculate the total number of years Fred has spent in his old age.
Fred has spent 28 years in his old age.
Step 2: Calculate the total number of years Fred has spent as a man.
Fred has spent half of his life as a man.
If we let x represent the total number of years Fred has lived, then x/2 = Fred's years as a man.
Step 3: Calculate the total number of years Fred has spent as a youth.
Fred has spent one-twelfth of his life as a youth.
If we let x represent the total number of years Fred has lived, then x/12 = Fred's years as a youth.
Step 4: Calculate the total number of years Fred has spent as a boy.
Fred has spent one-eighth of his life as a boy.
If we let x represent the total number of years Fred has lived, then x/8 = Fred's years as a boy.
Step 5: Calculate Fred's current age.
To find Fred's current age, we add up the years spent in each stage of his life: years as a boy, years as a youth, years as a man, and years in his old age.
Fred's current age = (x/8) + (x/12) + (x/2) + 28.
Step 6: Solve for x.
By simplifying the equation from step 5, we have:
Fred's current age = (3x + 2x + 24x + 672)/24.
Fred's current age = (29x + 672)/24.
Step 7: Solve for x by setting Fred's current age equal to x.
Fred's current age = (29x + 672)/24 = x.
To solve this equation, we can multiply both sides by 24:
24 * Fred's current age = 29x + 672.
Expanding the equation, we have:
24 * Fred's current age = 29x + 672.
24 * Fred's current age - 29x = 672.
24 * Fred's current age - 29/24 * x = 672.
Step 8: Substitute Fred's current age with a variable, let's use C.
24C - 29/24 * x = 672.
From this equation, we see that we need more information to determine Fred's exact age. We cannot solve for x or Fred's current age without additional information.
To find out Fred's current age, we need to analyze the information provided. Let's break it down into different stages of his life and calculate the duration of each:
1. Fred lived one-eighth of his life as a boy.
Let's denote Fred's total lifespan as "L". As a boy, he lived one-eighth of his life, meaning he spent L/8 years as a boy.
2. Fred lived one-twelfth of his life as a youth.
As a youth, he lived one-twelfth of his life, so he spent L/12 years as a youth.
3. Fred lived one-half of his life as a man.
As a man, Fred lived one-half of his life. Therefore, he spent L/2 years as a man.
4. Fred has spent 28 years in his old age.
The question states that Fred has already spent 28 years in his old age.
Now, let's combine all the information to find Fred's current age:
L = L/8 + L/12 + L/2 + 28
To solve this equation, we can find a common denominator, which is 24, to simplify the equation:
24L = 3L + 2L + 12L + 672 (multiplied all terms by 24 to eliminate fractions)
24L = 17L + 672
24L - 17L = 672
7L = 672
Finally, let's solve for L, which represents Fred's total lifespan:
L = 672 / 7
L = 96
Therefore, Fred's current age is 96 years old.